Order parameter overall

For folded proteins, relaxation data are commonly interpreted within the framework of the model-free formalism, in which the dynamics are described by an overall rotational correlation time rm, an internal correlation time xe, and an order parameter. S 2 describing the amplitude of the internal motions (Lipari and Szabo, 1982a,b). Model-free analysis is popular because it describes molecular motions in terms of a set of intuitive physical parameters. However, the underlying assumptions of model-free analysis—that the molecule tumbles with a single isotropic correlation time and that internal motions are very much faster than overall tumbling—are of questionable validity for unfolded or partly folded proteins. Nevertheless, qualitative insights into the dynamics of unfolded states can be obtained by model-free analysis (Alexandrescu and Shortle, 1994 Buck etal., 1996 Farrow etal., 1995a). An extension of the model-free analysis to incorporate a spectral density function that assumes a distribution of correlation times on the nanosecond time scale has recently been reported (Buevich et al., 2001 Buevich and Baum, 1999) and better fits the experimental 15N relaxation data for an unfolded protein than does the conventional model-free approach. 

This equation describes the orientation around a common axis called the director of the domain. For perfectly parallel orientation (P2) equals 1. The orientation of the directors in the solution is described by the order parameter PD. The overall orientational order of the anisotropic solution is given by... 

From these overall profiles, it is not easy to extract conformational properties, other than that it will be clear that the lipid molecules are strongly anisotropically oriented in the bilayer. For this, other characteristics are much more appropriate. It is possible to define an order parameter which indicates how much the lipid tails are oriented normal to the membrane ... 

Formally, S2 represents a decrease in the autocorrelation function caused by the motion S2=0 corresponds to completely unrestricted motion of a bond (N-H in this case), while S2=0 is expected if the bond reorientations are frozen. It was shown recently that the order parameter may be related to the statistical mechanical properties of a protein molecule [33-35] hence, changes in the NMR-derived order parameters can indicate localized contributions to overall molecular entropy. 

Up to this point only overall motion of the molecule has been considered, but often there is internal motion, in addition to overall molecular tumbling, which needs to be considered to obtain a correct expression for the spectral density function. Here we apply the model-free approach to treat internal motion where the unique information is specified by a generalized order parameter S, which is a measure of the spatial restriction of internal motion, and the effective correlation time re, which is a measure of the rate of internal motion [7, 8], The model-free approach only holds if internal motion is an order of magnitude (<0.3 ns) faster than overall reorientation and can therefore be separated from overall molecular tumbling. The spectral density has the following simple expression in the model-free formalism ... 

The success of these new multi-alignment approaches for the extraction of generalized order parameters from RDCs relies on a couple of fundamental assumptions. The first of these, as described in Section 2, is that the molecule is structured enough that the internal dynamics remain uncorrelated with the overall alignment. This corresponds to the assumption that the separation of averaging in Eq. (21) remains valid. If this does not hold, then overall alignment and internal motion will be convoluted in some nonlinear manner. The second assumption is that the structure and dynamics of the molecule is not influenced by change of medium. Provided that both of these assumptions are permissible, the acquisition of sufficient... 

Fig. 11. Dipolar generalized order parameters squared (S dc) determined using the DIDC approach for the protein ubiquitin (solid lines and circles). The shaded region represents the generalized order parameters squared determined using 15N spin relaxation methods.137 Due to the extended timescale sensitivity of RDCs, the overall scaling for the dipolar order parameters was chosen such that S. values were equal to or less than the corresponding spin relaxation order parameters.

Equation 37 has been used in an attempt130 to describe internal flexibility of the three hydroxymethyl groups of sucrose molecule in DzO solutions. The experimental data showed that the contribution of the overall motion to the spectral-density function of the hydroxymethyl group is similar to that of the ring carbons of sucrose. However, the presence of rapid internal motions about the three exocyclic bonds reduces the spectral density amplitudes. On the basis of the calculated order parameters in conjunction with model calculations, it was suggested130 that internal motions may be described as torsional librations. 

These symmetry characteristics of T7 and pairing order parameter. The overall symmetry is expected to be of a dx2 y2 type however, the sign reversal of T7 through the charged stripes, and the lack of coherence in the details of the dynamic stripe-like inhomogeneities between different Cu02 planes, is expected to result in features different from those of a simple (/A v -wavc pairing (especially when the... 

The value of the general order parameter S2 is between 0 and 1. Value 0 corresponds to totally unrestricted motion, while value 1 to fully restricted motion. As these parameters are commonly interpreted within the internal molecular reference frame,c the value of 1 means that the bond is constrained to a fixed orientation and all of its motions correspond to the overall tumbling of the molecule. 

In some polymers such segmental motions can be important, whereas in others (e.g., proteins) the overall skeleton is rigid, but there are rapid internal motions of moieties relative to the skeleton. In this case, relaxation and NOE data are often analyzed by the Lipari-Szabo formalism,96 which yields values for an overall correlation time rM, a correlation time for fast motions re, and a generalized order parameter S (see Eq. 7.16), which describes the amplitudes of the internal motions. 

The inclusion of an overall reaction order parameter greatly increases the correlation of the predicted and experimental viscosity profiles for highly crosslinked epoxy resin systems. 

Oscillations of were found in SFS multilayers for different combinations of materials [19-28]. Typically at small F layer thickness, d, phase difference

between phases of superconductor order parameters is zero (so-called zero state). With a increase exhibits first a rapid drop with a minimum for some df. After this point increases with df saturating at larger thickness. This overall TJ dj ) behavior is a signature of the 0 -phase shift in S/F hybrids [2]. At large d the critical temperature for = r exceeds for [Pg.538]

Figure 3.25. Ordering parameter for three overall densities in the monolayer simulated in fig. 3.24. (Redrawn from Kox et al., loc. cit.)...

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